The Curve Who Became a Witch: The Mathematics of Maria Gaetana Agnesi (1718-1799)

If any century would have favorably understood the manic blend of child shaming and twisted pride that is the typical Toddlers and Tiaras pageant parent, it was the Eighteenth. Child prodigies were in, and if you were aching to claw your way into the ranks of the minor nobility, your precocious son or daughter was your meal ticket. Some decades before Leopold Mozart dragged young Wolfgang to any prince or archbishop who had half a chance of offering a decent appointment, a Milanese girl with a genius intellect was made the center of an ongoing academic circus routine by her status-hunting father.

She would go on to write one of the first comprehensive calculus textbooks in Italian, and then suddenly forsake all scientific study to devote herself completely to the well-being of the poor and elderly. She was Maria Gaetana Agnesi, remembered today only for a curve, the Witch of Agnesi, which shows up in the margins of introductory calculus texts from time to time, and which she didn’t actually discover. In her own age, though, she was recognized as an intellectual wonder of the world. Born in 1718 in Milan to a merchant family with big dreams of gaining entrance to the nobility, she and her sister were from the first given an intensive education by a series of top-notch tutors. Maria showed an early genius for languages, philosophy, science, and mathematics, while her sister attained renown for her musical compositions.

Their father, Pietro, a spendthrift of the most abject order, saw in them his ticket to greatness. His plan was two-fold: (1) Spend money as ostentatiously as possible to get the nobles to respect him, and (2) Arrange a series of entertainments for the religious and noble orders with his children as the stars. These were the famed Agnesi conversazioni, in which the young Maria would be seated at the center of a circle of onlookers, and instructed to answer any question about any topic that might come to their minds, in any language they chose. She knew seven languages by her tenth birthday, could compose academically rigorous defenses to proffered theses on the fly, and hated every moment of it.

She was reserved by nature, and the strain of her performances plunged her into a serious illness at the age of eleven. While in the depths of her sickness, she was offered religious instruction by priests from the Theatine order whose approval her father was seeking. They took the overworked, sick girl and threw on her shoulders an ascetic regimen that taught the denigration of worldly emotions and a selfless devotion to pure intellectual effort and tireless charity.

She got better, and credited their regime with her recovery. She renounced her earlier philosophical speculation and scientific curiosity, and plunged into the realms of pure mathematics, social work, and theology. It was a program well fitted to the principles of the Milanese Catholic Enlightenment – an odd amalgam that attempted to hold together a profound admiration for the accomplishments of Galilean and Newtonian science with a fundamental belief in the basic correctness of the Catholic faith. They sought to live a life of unrestrained intellectual curiosity augmented by a service-centered approach to religious life.

The Catholic Enlightenment was full of interesting and well-meaning ideas that were destined to satisfy nobody. Agnesi divided her time between working at an elderly-care hospital and writing a two-volume textbook that sought to synthesize and explain, for the first time in Italian, the insights of analytic geometry and calculus. The work, Instituzioni analitiche, was finally published in 1748 and made her an academic star, resulting in an invitation to join the faculty at the famous University of Bologna, where Laura Bassi also served as a professor of physics.

The book itself is something of a curiosity. It was Agnesi’s opinion that the application of calculus to physical problems was profoundly uninteresting because it was merely worldly, and so her book intentionally leaves out many of the advances attained by Continental mathematicians of the Leibnizian tradition in favor of a return to Cartesian and Newtonian geometric arguments. The English and Catholics, predictably, loved it, while others viewed it as a noble relic, the last and best effort of a tradition that decidedly did not have the wind at its back. It was the summit of an approach to mathematics that would soon be swallowed by the analytic power of Lagrange and Euler, and perhaps the most important scientific work to come out of the Italian Catholic Enlightenment.

And it was the last thing Agnesi wrote publicly about mathematics. The book done, she retired completely into her charity and religious work. For the remaining fifty years of her life, she gave comfort to the mentally ill and elderly as the director of the Pio Albergo Trivulzio from 1771, and hunted the streets for children to be brought to her catechism class. The woman who had been regarded as one of the greatest minds of Italy, consulted from every corner of Europe for her advice on matters mathematical and philosophical, died unremarked in 1799.

FURTHER READING: The major book available on Agnesi is The World of Maria Gaetana Agnesi, Mathematician of God, by Massimo Mazzotti. It is under-long, over-priced, and in general, I do not like it. It represents that academic tradition wherein the mad desire to win fame by coining a trendy theory gets in the way of equitably assessing the material at hand. There are some good and interesting slices of history we would not have seen except through Mazzotti’s research, but there is always a lurking theory-born torsion twisting the sources in a way that makes you not quite trust the conclusions, such as they are. Unless you are particularly curious about the secondary and tertiary figures who had a hand in the Milanese Catholic Enlightenment, you’re probably better off looking at some of the briefer lives of Agnesi, like that in Lynn Osen’s Women in Mathematics.

And for more awesome Women in Science comics, check out the archive and my books, Illustrated Women in Science – Volume 1, 2 and 3.

Dale DeBakcsy is the writer and artist of the Women In Science and Cartoon History of Humanism columns, and has, since 2007, co-written the webcomic Frederick the Great: A Most Lamentable Comedy with Geoffrey Schaeffer. He is also a regular contributor to The Freethinker, Philosophy Now, Free Inquiry, and Skeptical Inquirer. He studied intellectual history at Stanford and UC Berkeley before becoming a teacher of mathematics and drawer of historical frippery.